On multichannel signal detection
- Ingster, Yuri I.
- Lepskii, Oleg V.
2010 Mathematics Subject Classification
- 62G10 62G20
- Multichannel signal detection, minimax hypothesis testing, adaptive hypothesis testing, distinguishability conditions.
We consider $n$-channel signal detection system. Each $i$th channel could contain (or not contain) a signal. We suppose a signal is a function $f_i(t), tin (0,1)$ observing in the white Gaussian noise of level $e>0$. Let $k$ be a number of channels which contain the signals. This number could be known or unknown. The functions $f_i$ could be known or unknown as well. If shapes of functions $f_i$ are unknown, then we consider nonparametric case. We suppose that functions $f_i$ belongs to the Sobolev ball $S^sigma$ where the smoothness parameter $sigma>0$ could be known or unknown as well. The cases, when $k$ or $sigma$ are unknown, lead to the ädaptive" problems. We are interested in the following problems:
- How large the signals $f_i$ should be in order to detect these signals with vanishing errors, as the number of channels $n$ tends to infinity?
- What are the structures of test procedures which provide the detection of signals with the vanishing errors, if it is possible?